Numerical Methods for Maxwell's Equations in Inhomogeneous Media with Material Interfaces

Abstract

In this paper, we will present some recent results on developing numerical methods for solving Maxwell's equations in inhomogeneous media with material interfaces. First, we will present a second order upwinding embedded boundary method — a Cartesian grid based finite difference method with special upwinding treatment near the material interfaces. Second, we will present a high order discontinuous spectral element with Dubinar orthogonal polynomials on triangles. Numerical results on electromagnetic scattering and photonic waveguide will be included.